飞机上的分子蜘蛛
Molecular Spiders on the Plane
摘要：
合成生物分子蜘蛛的“腿”由单链DNA片段组成，当底物DNA与腿DNA互补时，它可以在被称为底物的单链DNA片段覆盖的表面上移动。如果蜘蛛的运动不影响基板，蜘蛛的行为渐近随机游走。研究了蜘蛛在正方形网格上移动时的扩散系数和访问站点数。蜘蛛的腿跳到最近的邻居网站的约束，任何两个腿之间的距离不能超过一个最大跨度。我们建立了双足蜘蛛的解析结果，并研究多足蜘蛛的数值。在实验实现中，腿通常将基板转化为产品（访问站点）。腿与产品的结合较弱，因此从基板的跳跃率较小。这使得问题的非马尔可夫，我们调查它的数字。我们展示了一种反直觉行为的出现--在未访问的网站上，蜘蛛的速度越慢，它们就越活跃。
英文摘要：
Synthetic bio-molecular spiders with "legs" made of single-stranded segments of DNA can move on a surface covered by single-stranded segments of DNA called substrates when the substrate DNA is complementary to the leg DNA. If the motion of a spider does not affect the substrates, the spider behaves asymptotically as a random walk. We study the diffusion coefficient and the number of visited sites for spiders moving on the square lattice with a substrate in each lattice site. The spider's legs hop to nearest-neighbor sites with the constraint that the distance between any two legs cannot exceed a maximal span. We establish analytic results for bipedal spiders, and investigate multileg spiders numerically. In experimental realizations legs usually convert substrates into products (visited sites). The binding of legs to products is weaker, so the hopping rate from the substrates is smaller. This makes the problem non-Markovian and we investigate it numerically. We demonstrate the emergence of a counter-intuitive behavior - the more spiders are slowed down on unvisited sites, the more motile they become.
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